Solid-solid phase transitions with space-dependent wells

2026/07/16 by Elisa Davoli, Jakob Deutsch, Manuel Friedrich +1
#math.AP

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Abstract

We investigate a second-order Modica-Mortola functional of the form E_ε[u] := ∫_Ω(1)/(ε) W(x, ∇ u) + ε|∇² u|² dx, which models solid--solid phase transitions in heterogeneous media. We neglect the assumption of frame indifference in the elastic energy density W while allowing for space-dependent, pointwise-compatible wells. Under suitable assumptions on W and regularity conditions on the associated rank-one connection, we prove that E_ε Γ-converges to a local interfacial energy defined for suitable laminate-type configurations.

Citations

• Fine phase mixtures as minimizers of energy

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